To what extent can quantum computers help to develop Artificial Intelligence?
Quantum computers are super awesome at matrix multiplication, with some limitations. Quantum superposition allows each bit to be in a lot more states than just zero or one, and quantum gates can fiddle those bits in many different ways. Because of that, a quantum computer can process a lot of information at once for certain applications.

One of those applications is the Fourier transform, which is useful in a lot of problems, like signal analysis and array processing. There's also Grover's quantum search algorithm, which finds the single value for which a given function returns something different. If an AI problem can be expressed in a mathematical form amenable to quantum computing, it can receive great speedups. Sufficient speedups could transform an AI idea from "theoretically interesting but insanely slow" to "quite practical once we get a good handle on quantum computing."